Question: Given $ m \angle LOM = 9x - 52$, and $ m \angle MON = 3x + 40$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {9x - 52} + {3x + 40} = {180}$ Combine like terms: $ 12x - 12 = 180$ Add $12$ to both sides: $ 12x = 192$ Divide both sides by $12$ to find $x$ $ x = 16$ Substitute $16$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 9({16}) - 52$ Simplify: $ {m\angle LOM = 144 - 52}$ So ${m\angle LOM = 92}$.